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The Stick-Breaking Construction of the Beta Process as a Poisson Process

Statistics Theory 2012-04-20 v2 Probability Machine Learning Statistics Theory

Abstract

We show that the stick-breaking construction of the beta process due to Paisley, et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying representation to derive error bounds on truncated beta processes that are tighter than those in the literature. We also develop a new MCMC inference algorithm for beta processes, based in part on our new Poisson process construction.

Keywords

Cite

@article{arxiv.1109.0343,
  title  = {The Stick-Breaking Construction of the Beta Process as a Poisson Process},
  author = {John Paisley and David Blei and Michael I. Jordan},
  journal= {arXiv preprint arXiv:1109.0343},
  year   = {2012}
}

Comments

We've updated with the conference version of the paper. Please note that the title has changed

R2 v1 2026-06-21T18:58:41.312Z